The deal is expected to be for the prorated league minimum. Coach Marvin Lewis said Monday that Johnson would be fourth on the team's depth chart at running back.

"That's what his role would be, it would be as a fourth running back and an opportunity as a backup player on this football team doing all the things backup players do, and that's work their tails off in the kicking game and showing looks [on the scout team] and so forth that way," Lewis said. "And then he would be an insurance policy if something would happen down the line to one of our guys where he'd have a chance to be active.

"But I couldn't foresee him being active when he was initially here, if this is what happens. And that's what I've told him."

The Bengals, along with several other teams, first expressed interest in Johnson last week as depth behind Cedric Benson, who strained a hip muscle in Sunday's 18-12 win in Pittsburgh that left the Bengals (7-2) in control of the AFC North.

Benson is expected to practice on a limited basis this week. Lewis said there's a chance he could play Sunday in Oakland.

Lewis assured Benson that the Bengals' interest in Johnson would have no effect on his status as the primary runner. Lewis said he first spoke with Johnson by phone last Thursday, before Benson's injury.

"I had a chance to visit with Cedric about this, that it doesn't affect him -- zero," Lewis said. "This was under way last week, so Cedric [being injured] in the game had no effect on this thing."

The Chiefs released Johnson last Monday, the day he was due back from his second (two-week) suspension in the past 12 months. His last brush with controversy came two weeks ago when he posted on his Twitter account a gay slur, insulted followers and questioned the competence of head coach Todd Haley.

Since rushing for a team-record 1,789 yards on an NFL-record 416 carries in 2006, Johnson was never quite the same in Kansas City.

In 2008, then-coach Herm Edwards benched him for three straight games for violating team rules and NFL commissioner Roger Goodell suspended him a fourth game for violating the league's player conduct policy.

Johnson was later sentenced to two years' probation after pleading guilty to two counts of disturbing the peace. One woman accused him of throwing a drink on her and another said he had pushed her head at a Kansas City nightspot.

After his huge year in '06, Johnson stayed away from training camp, demanding more money, and he got it, a six-year deal worth $45 million, including $19 million guaranteed.

But hampered by a foot injury, he wound up with only 559 yards and three touchdowns. In 2008, he ran for 874 yards as the Chiefs sank to 2-14. Still, Johnson was only 75 yards away from breaking Priest Holmes' team rushing record when the team let him go.

ESPN NFL Insider Adam Schefter and ESPN NFL reporter Michael Smith contributed to this report. Information from The Associated Press was used in this report.